Effects of tricritical points and morphotropic phase boundaries on the piezoelectric properties of ferroelectrics

Abstract

The longitudinal piezoelectric coefficient d * 33 of a PZT-like ferroelectric is computed in the full compositiontemperature parameter space using sets of parameters which control the position of the tricritical points and the degree of tilting of the morphotropic phase boundary separating the ferroelectric rhombohedral phase from the ferroelectric tetragonal phase. The system is modeled using a Ginzburg-Landau expansion of the free energy in terms of the electric polarization up to sixth order, including all the symmetry allowed terms. We obtain two regions of the phase diagram with a large piezoelectric response. In the polar direction, d * 33 is large in the vicinity of the paraelectric to ferroelectric line of phase transitions, whereas in a nonpolar direction d * 33 is large in the vicinity of the morphotropic phase boundary. We find that a given degree of tilting of the morphotropic phase boundary can be obtained from free energies with different degrees of anisotropy, and therefore the titling and anisotropy are not directly related . On the other hand, the piezoelectric response is larger when the two tricritical points of the phase diagram are farther apart from each other than when they collapse onto a single tricritical point.

Accelerated search for BaTiO 3 -based piezoelectrics with vertical morphotropic phase boundary using Bayesian learning

“…We also know from Landau theory that γ2 in Eq. 1 stabilizes the T phase with respect to the R phase, whereas γ3 stabilizes the R phase relative to the T phase, thereby influencing the relative tilting affecting the MPB curvature (16). Although d33 is generally large in the vicinity of the MPB, and a given degree of tilting can result from free energies with different degrees of anisotropy, the latter are difficult to relate directly.…”

“…Piezoelectric materials, such as the solid solutions of BaTiO3, are best suited for exploring Bayesian inference methods because historically they are well modeled by Landau-Devonshire theory (12)(13)(14) and equations exist for describing some of the key characteristics that determine the functional response, such as the morphotropic phase boundary (MPB) (15,16). These equations serve as "constraints" that encode prior knowledge within our Bayesian formalism.…”

Antiferroelectric–ferroelectric phase boundary enhances polarization extension in rhombohedral Pb(Zr,Ti)O3

“…The corresponding polarization change is between tetragonal polarization P T ¼ ð0; 0; P T Þ and rhombohedral polarization P R ¼ ðP R ; P R ; P R Þ= ffiffi ffi 3 p . With jP T j % jP R j in the MPB region, 11,12 the dominant change of the polarization vector along P T $ P R path is rotation. The enhanced material coefficients are therefore transverse dielectric susceptibility, v 11 , and shear piezoelectric coefficients, e.g., d 15 .…”

“…7,8,20 Thus, the 6th order LGD function can be used to describe qualitatively many relevant features of the PZT across the composition-temperature phase diagram without affecting general validity of the results. Porta and Lookman 12 have, for example, recently analysed effects of triple and critical points and temperature dependence of MPB on the piezoelectric properties of PZT using even a more restricted LGD approach. In addition, we calculate only properties for x !…”

Phase coexistence in ferroelectric solid solutions: Formation of monoclinic phase with enhanced piezoelectricity

“…Such knowledge is critical for seeking new systems of piezoelectric materials, especially non-toxic lead free piezoelectrics. 1,10,11 Lead-based ferroelectric single crystal solid solutions, such as PbZr 1-x Ti x O 3 (PZT), Pb(Mg 1/3 Nb 2/3 )O 3 -PbTiO 3 (PMN-PT) and Pb(Zr 1/3 Nb 2/3 )O 3 -PbTiO 3 (PZN-PT) systems, are still dominating piezoelectric materials due to their extremely high performance. [12][13][14] Physical properties of ferroelectric materials are closely related to the phase morphology boundaries and phase transition points, where the potential well is shallow and the energy barrier between two phases becomes very small.…”